For 3D fractional Navier-Stokes with transport noise and very weak diffusion, α below about 8.7e-9, infinitely many Hölder-continuous Leray-Hopf solutions share one deterministic initial condition up to a positive stopping time.
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Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise
For 3D fractional Navier-Stokes with transport noise and very weak diffusion, α below about 8.7e-9, infinitely many Hölder-continuous Leray-Hopf solutions share one deterministic initial condition up to a positive stopping time.